A254717 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 9's.

0, 12, 11, 36, 99, 207, 629, 3982, 13216, 24090, 65698, 131076, 176801, 2074822, 5203944, 3716991

Offset: 0

Author

Martin Y. Champel, Feb 06 2015

Keywords

• nonn
• more
• base

Examples

			a(1) = 12 since 12! = 479001600 contains '9' and 12 is the smallest integer for which the condition is met,
a(2) = 11 since 11! = 39916800 contains '99' and 11 is the smallest integer for which the condition is met.
		

Crossrefs

Cf. A254042, A254447, A254448, A254449, A254500, A254501, A254502, A254716.

Programs

Mathematica

A254717[n_] := Module[{m = 0},
   If[n == 0, While[MemberQ[IntegerDigits[m!], 9], m++]; m,
    t = Table[9, n];
    While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m]];
Table[A254717[n], {n, 0, 7}] (* Robert Price, Mar 21 2019 *)

PARI

a(n)=k=0;while(k<10^4,d=digits(2*10^(#(digits(k!))+1)+10*k!);for(j=1,#d-n+1,c=0;for(i=j,j+n-1,if(d[i]==9,c++);if(d[i]!=9,c=0;break));if(c==n&&d[j+n]!=9&&d[j-1]!=9,return(k)));if(c==n,return(k));if(c!=n,k++))
for(n=1,6,print1(a(n),", ")) \\ Derek Orr, Feb 06 2015

Extensions

a(12) from Jon E. Schoenfield, Feb 21 2015

a(13)-a(15) from Bert Dobbelaere, Oct 29 2018